Related papers: Second order stochastic gradient update for Choles…
Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…
This paper deals with the problem of estimating second-order parameter sensitivities for stochastic reaction networks, where the reaction dynamics is modeled as a continuous time Markov chain over a discrete state space. Estimation of such…
The reparameterization trick is widely used in variational inference as it yields more accurate estimates of the gradient of the variational objective than alternative approaches such as the score function method. Although there is…
In this paper we investigate the convergence properties of a variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Our study is based on the recent theoretical foundation that the pure rank-mu update CMA-ES performs the…
In this paper the elicitation of probabilities from human experts is considered as a measurement process, which may be disturbed by random 'measurement noise'. Using Bayesian concepts a second order probability distribution is derived…
The performance of standard stochastic approximation implementations can vary significantly based on the choice of the steplength sequence, and in general, little guidance is provided about good choices. Motivated by this gap, in the first…
Ionides, King et al. (see e.g. Inference for nonlinear dynamical systems, PNAS 103) have recently introduced an original approach to perform maximum likelihood parameter estimation in state-space models which only requires being able to…
Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a Markov chain with a stationary distribution. With this perspective, we derive several new results. (1) We show that constant SGD can be used as an…
Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an expectation of a test function along the sample path of a…
Recently, many machine learning and statistical models such as non-linear regressions, the Single Index, Multi-index, Varying Coefficient Index Models and Two-layer Neural Networks can be reduced to or be seen as a special case of a new…
This work presents a multilevel variant of Stein variational gradient descent to more efficiently sample from target distributions. The key ingredient is a sequence of distributions with growing fidelity and costs that converges to the…
Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (continuous or discrete) parametric…
In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient…
A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…
Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior…
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…
For approximating a target distribution given only its unnormalized log-density, stochastic gradient-based variational inference (VI) algorithms are a popular approach. For example, Wasserstein VI (WVI) and black-box VI (BBVI) perform…
We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates…
Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…
Assuming a banded structure is one of the common practice in the estimation of high-dimensional precision matrix. In this case, estimating the bandwidth of the precision matrix is a crucial initial step for subsequent analysis. Although…